{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import gym\n",
    "import itertools\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import sys\n",
    "\n",
    "if \"../\" not in sys.path:\n",
    "  sys.path.append(\"../\") \n",
    "\n",
    "from collections import defaultdict\n",
    "from lib.envs.cliff_walking import CliffWalkingEnv\n",
    "from lib import plotting\n",
    "\n",
    "matplotlib.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "env = CliffWalkingEnv()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_epsilon_greedy_policy(Q, epsilon, nA):\n",
    "    \"\"\"\n",
    "    Creates an epsilon-greedy policy based on a given Q-function and epsilon.\n",
    "    \n",
    "    Args:\n",
    "        Q: A dictionary that maps from state -> action-values.\n",
    "            Each value is a numpy array of length nA (see below)\n",
    "        epsilon: The probability to select a random action. Float between 0 and 1.\n",
    "        nA: Number of actions in the environment.\n",
    "    \n",
    "    Returns:\n",
    "        A function that takes the observation as an argument and returns\n",
    "        the probabilities for each action in the form of a numpy array of length nA.\n",
    "    \n",
    "    \"\"\"\n",
    "    def policy_fn(observation):\n",
    "        A = np.ones(nA, dtype=float) * epsilon / nA\n",
    "        best_action = np.argmax(Q[observation])\n",
    "        A[best_action] += (1.0 - epsilon)\n",
    "        return A\n",
    "    return policy_fn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def q_learning(env, num_episodes, discount_factor=1.0, alpha=0.5, epsilon=0.1):\n",
    "    \"\"\"\n",
    "    Q-Learning algorithm: Off-policy TD control. Finds the optimal greedy policy\n",
    "    while following an epsilon-greedy policy\n",
    "    \n",
    "    Args:\n",
    "        env: OpenAI environment.\n",
    "        num_episodes: Number of episodes to run for.\n",
    "        discount_factor: Gamma discount factor.\n",
    "        alpha: TD learning rate.\n",
    "        epsilon: Chance to sample a random action. Float between 0 and 1.\n",
    "    \n",
    "    Returns:\n",
    "        A tuple (Q, episode_lengths).\n",
    "        Q is the optimal action-value function, a dictionary mapping state -> action values.\n",
    "        stats is an EpisodeStats object with two numpy arrays for episode_lengths and episode_rewards.\n",
    "    \"\"\"\n",
    "    \n",
    "    # The final action-value function.\n",
    "    # A nested dictionary that maps state -> (action -> action-value).\n",
    "    Q = defaultdict(lambda: np.zeros(env.action_space.n))\n",
    "\n",
    "    # Keeps track of useful statistics\n",
    "    stats = plotting.EpisodeStats(\n",
    "        episode_lengths=np.zeros(num_episodes),\n",
    "        episode_rewards=np.zeros(num_episodes))    \n",
    "    \n",
    "    # The policy we're following\n",
    "    policy = make_epsilon_greedy_policy(Q, epsilon, env.action_space.n)\n",
    "    \n",
    "    for i_episode in range(num_episodes):\n",
    "        # Print out which episode we're on, useful for debugging.\n",
    "        if (i_episode + 1) % 100 == 0:\n",
    "            print(\"\\rEpisode {}/{}.\".format(i_episode + 1, num_episodes), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "        \n",
    "        # Implement this!\n",
    "    \n",
    "    return Q, stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 500/500."
     ]
    }
   ],
   "source": [
    "Q, stats = q_learning(env, 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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4derUSUeOHFFBQYFiYmK0ZcsWTZ8+3WdMUlKSNm/erM6dO2vbtm3eYNerVy+98847Ki8v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\nVkREhEaPHq1Zs2bJZrPpjjv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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a3839b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+U7e62n+dO3fG2LFjcfTo0btdSp1WV/uPbk9tfffXX39h8ODBDH3/X037r84E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\niNjEvwCXctN9U+ogMQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a3bb908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PrUfPrRcdHV0r66mXq1wBAABQewh0AAAANkegAwAAsDkCHQAAgM0R6AAAAGyO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\nsDkCHQAAgM39P+XhbrHG6s8eAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a53d0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotting.plot_episode_stats(stats)"
   ]
  },
  {
   "cell_type": "code",
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